A. \(33\frac{2}{6}\)

B. \(36\frac{8}{3}\)

C. \(34\frac{4}{2}\)

D. \(31\frac{5}{7}\)

**Answer:**

**D. \(31\frac{5}{7}\)**

**Solution:**

A. \(33\frac{2}{6}\)

B. \(36\frac{8}{3}\)

C. \(34\frac{4}{2}\)

D. \(31\frac{5}{7}\)

**Answer:**

**D. \(31\frac{5}{7}\)**

**Solution:**

A. Rs. 5081

B. RS. 4810**C. RS. 4991**

D. Rs. 4972

**Solution:**

A. 84 kg

B. 81 kg

C. 80 kg**D. 85 kg**

**Solution:**

\[\left. \begin{array} { l }\text {Average weight of each person = 65kg} \\ \text {Avg weight of each person increased = }2.5kg\\ \text {Total avg weight of 8 persons increased by:} \\ 8\times2.5=20kg\\ \text {Since total weight increased is actually} \\ \text {the weight of new person. Therefore,}\\ \text { The weight of new person = 65+20= 85KG}\\ \end{array} \right.\]

A. 20 years

B. 27 years

C. 21 years**D. 23 years**

**Solution:**

\[\left. \begin{array} { l }\text {Avg monthly income of P and Q =5050 }\\
\text {Sum of incomes of P and Q is:}\\
\text {Avg income =} \frac{\text {Sum of Incomes}}{\text {Total Number of persons}}\\
\Rightarrow \text {5050 =} \frac{P+Q}{2}\\
\text {P+Q = 5050}\times 2\text {= 10100 …(i)}\\
\text {Likewise:}
\text {Q+R = 6250}\times 2\text {= 12500 …(ii)}\\
\text {P+R = 5200}\times 2\text {= 10400 …(iii)}\\
{ \text { Now adding (i), (ii) and (iii), we get: }}\\
\Rightarrow { 2 ( P + Q + R ) = 33000}\\
\text { P + Q + R= 16500 …(iv) } \\ { \text { Subtracting (ii) from (iv), we get } P = 4000 } \\ { \therefore \text { P’s monthly income } = \text { Rs. } 4000 }
\end{array} \right.\]

A. 8.71**B. 7.98**

C. 6.87

D. 9.99

\[\left. \begin{array} { l } \text {Total expenditure on petrol each year = 4000}\\ \text {Petrol consumption in 1st year = }\frac{4000}{7.5}\\ \text {Petrol consumption in 2nd year = }\frac{4000}{8}\\ \text {Petrol consumption in 3rd year = }\frac{4000}{8.50}\\ \text {Total quantity of petrol consumed in 3 years:}\\ \Rightarrow ( \frac { 4000 } { 7.50 } + \frac { 4000 } { 8 } + \frac { 4000 } { 8.50 } ) \text { litres } \\ { = 4000 ( \frac { 2 } { 15 } + \frac { 1 } { 8 } + \frac { 2 } { 17 } ) \text { litres } }\\ {= ( \frac { 76700 } { 51 } ) \text { litres } }\\ { \text { Total amount spent } = \text { RS. } ( 3 \times 4000 )}\\ {= \text { Rs. } 12000 \text { . } } \\ { \therefore \text { Average cost } = \text { Rs. } ( \frac { 12000 \times 51 } { 76700 } ) }\\ {\text {= Rs. } \frac { 6120 } { 767 } = Rs 7 .98 } \end{array} \right.\]

A. 29 kg

**B. 31 kg**

C. 40 kg

D. 12 kg

**Solution:**

Let A, B, C represent their respective weights. Then, we have:

\[\left. \begin{array} { l } { A + B + C = ( 45 \times 3 ) = 135 \ldots . \text { (i) } } \\ { A + B = ( 40 \times 2 ) = 80 \ldots . \text { (ii) } } \\ { B + C = ( 43 \times 2 ) = 86 \ldots \text { (iii) } } \\ { \text { Adding (ii) and (iii), we get: } A + 2 B + C }\\

{= 166 \ldots \text { (iv) } } \\ { \text { Subtracting (i) from (iv), we get: } B = 31 . } \\ { \therefore \text { B’s weight } = 31 kg \text { . } } \end{array} \right.\]